W3 Total Cache + BuddyPress causing log in/log out issues

There’s an issue when using page cache that doesn’t appear to log users out properly. When logging in, it sometimes still shows the “log in” link as if the user isn’t logged in and other times it doesn’t let the user log out.

Disabling “Don’t cache pages for logged in users” fixes the issue, but I was wondering if it would be possible to get this to work properly without disabling page cache for logged in users?

I’m not sure if it’s possible, but why would you want page cache?
Using it means your members will be looking at stale pages.
For example Users A & B are online.
User A creates some content (update, comment, etc)
User B won’t see it until they log-out, log-in.